# Tagged Questions

**4**

votes

**1**answer

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### Geodesic flow on infinite surfaces

The geodesic flow on a compact hyperbolic surface (i.e. a surface with a riemannian metric of constant curvature $-1$) has been well-studied, in particular it has been known for a long time that it is ...

**4**

votes

**1**answer

244 views

### Besides the tracioid are there other surfaces of revolution that have a constant negative curvature?

There is no surface in $ R^3 $ that can represent the complete hyperbolic plane (Hilberts theorem) so we always have to do with a surface that is not completely equivalent, has a cusp somewhere, but ...

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### Geodesics on the twisted pseudosphere (Dini's surface)

I wonder how difficult it is to compute geodesics on Dini's Surface,
a twisted pseudosphere?
Here is one parametrization, from
Alfred Gray's Modern Differential Geometry of Curves and Surfaces, ...

**2**

votes

**1**answer

714 views

### How to rigorously prove that simple closed curves on a surface are primitive closed curves ?

Let me first state the definitions :
A not-nullhomotopic closed curve / loop $c$ on an orientable surface $X,c:[0,1]\to X$ is called simple closed curve is $c|[0,1)$ is injective and [ $c(0)=c(1) ] ...